Collusion between firms in an oligopoly is a classic example of practical application of game theory in economics. We can almost directly utilize the model of the "Prisoner's Dilemma" to understand some of the results of such collusion, and why it has been made illegal in many countries, including the United States

The Prisoner's Dilemma is a prime demonstration of the value of information and communication of that information in a decision-making process where the agents are not completely independent of one another. In other words, the outcome of a decision by one agent will influence and "weight" the decision of another if they are able to collude.

The dominant strategy refers to the best choice that can be made by an agent with the available information that best serves that agent's self-interest. What occurs in the Prisoner's Dilemma is that an outside factor which can only be known if the agents are allowed to communicate with one another exists which makes available a better choice for both agents than that of their own dominant strategy. Thus, their self-interested choice will actually put them in a worse situation because there exists a possibility dependent on the outcome of both of their individual choices.

The real-world application which I learned of was the decision by firms in an oligopoly to cut or maintain price. A simple scenario will demonstrate this. In our example, an oligopoly consisting of Firm A and Firm B will make the cut/maintain decision.

We can characterize the implications of their decisions in this hypothetical scenario with a simple matrix:

```             FIRM B
cut    maintain
_________________
|        |        |
F      | B=\$0   | B=\$-100|
I cut  | A=\$0   | A=\$150 |
R      |        |        |
M      |--------+--------|
|        |        |
mntn | B=\$150 | B=\$50  |
A      | A=\$-100| B=\$50  |
|________|________|
```
• The dominant strategy for A is to cut price (avoiding a \$100 loss).
• The dominant strategy for B is to cut price (avoiding a \$100 loss).

Both avoid loss, but had both chosen to maintain price, they each would gain \$50.

Because the firms are unable to communicate, they cannot make such a decision, since they each would risk losing \$100 if the other firm did not choose accordingly. As they cannot "fix" the outcome by agreeing to maintain price, they get a suboptimal outcome.

Within the United States, collusion and the price-fixing which it allows (which can have both positive and negative consequences to consumers) are illegal. In practice, one of the methods which has developed within oligopoly-characterized industries is price leading, wherein a particular pricing pattern allows one firm to establish a market price informally, by making their decision public and thus serving as a sign to the rest of the industry.

Firms which are allowed to collude in an oligopoly tend to become cartels. The Prisoner's Dilemma, applied to a cartel, should ideally produce monopoly-like behavior, but cartels have a (usually strong) incentive to cheat (i.e. overproducing their agreed-upon quota to gain short-term benefit.) Cartels are considered unstable and prone to wars because of this tendency.

Col*lu"sion (?), n. [L. collusio: cf. F. collusion. See Collude.]

1.

A secret agreement and cooperation for a fraudulent or deceitful purpose; a playing into each other's hands; deceit; fraud; cunning.

The foxe, maister of collusion. Spenser.

That they [miracles] be done publicly, in the face of the world, that there may be no room to suspect artifice and collusion. Atterbury.

By the ignorance of the merchants or dishonesty of the weavers, or the collusion of both, the ware was bad and the price excessive. Swift.

2. Law

An agreement between two or more persons to defraud a person of his rights, by the forms of law, or to obtain an object forbidden by law.

Bouvier. Abbott.

Syn. -- Collusion, Connivance. A person who is guilty of connivance intentionally overlooks, and thus sanctions what he was bound to prevent. A person who is guilty of collusion unites with others (playing into their hands) for fraudulent purposes.

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